1. Field of the Invention
The present invention relates to a model parameter determining method for various models in a engineering field, and more specifically to a model parameter determination program and a model parameter determination apparatus for obtaining a possible range, etc. of a feasible parameter by applying a quantifier elimination algorithm to a constraint expression generated based on, for example, a model of a simulation of a biological system and variable data.
2. Description of the Related Art
The present invention processes an application problem in a wide range represented by a first order predicate logic expression, that is, an expression with a quantifier, in various engineering fields. In the explanation below, the contents of the present invention are explained mainly by referring to the application in a simulation of a biological system.
It has been demanded to efficiently determine a parameter of a model in a field of analyzing and designing a biological system by performing a simulation on various systems relating to a living object and a cell, that is, a model of a biological system, for example, a model of a glycolytic reaction, etc.
Therefore a problem to be dealt with in the present invention is to grasp the property or the entity of a biological system based on the model when a time-series data for some variables of a biological system, which is obtained from a numerical simulation via a model (ex. HPN) or experimental observation, is given. Practically, for example, the feasible range of a reaction coefficient as a parameter of a model is obtained, a feasible area of common parameters is obtained when some actually measured values of a parameter of a model are obtained, the existence of a feasible value of parameters of a model is confirmed, and new findings about a biological system are detected.
With the study of biotechnology growing actively, the development of effective solution means for satisfying the above-mentioned objects is strongly demanded. The means is required in various fields in, for example, finding the biological system designing process in the industry, for example, finding the mechanism of the crisis of disease, and in the preventive medicine, tailor-made medicine, etc. However, the existing technology has no effective methods for satisfying the above-mentioned demand. Therefore, some tools have been used for performing numerical simulations by structuring a model of a simulation of a biological system, for example, a genomic object net (GON), a visual object net (VON), E-CELL, etc. to set various parameter values, repeat numerical simulations, determining the value of a parameter desired by trial-and-error, and estimating the property of the system, thereby requiring an exceedingly laborious operation.
Relating to the hybrid Petri net for use in the above-mentioned modeling operation, the genomic object net and visual object net as a tool for simulation, the following documents and thesis are presented. However, the contents of these documents are not directly related to the present invention, the detailed explanation is omitted here.
[Non-Patent Literature 1]
www genomicobject.net/member—3/index.html,
“Genomic Object Net Projects”, Jul. 9, 2004
[Non-Patent Literature 2]
www.genome.ib.sci.yamaguchi-u.ac.jp/˜atsushi/phase/karui00.pdf, “Induction of λ Phage and Representation of Inverse Adjustment Mechanism by Hybrid Petri Net”, Jul. 9, 2004
[Non-Patent Literature 3]
www.Systemtechnik.tu-i1menau.du/˜drath/visual_E.htm, “Visual Object Net ++”, Jul. 9, 2004
FIG. 1 is an explanatory view of the existing system of a simulation of a biological system. In FIG. 1, for example, a model is generated using the hybrid Petri net, etc. on a glycolytic system, a numerical simulation is repeatedly performed on the values of various parameters using a simulation tool on the model, thereby designing a biological system in the trial-and-error system and understanding the entity of a biological system.
However, in the above-mentioned method, there have been the problems that choice of parameter values to be examined simply depends on the knowledge and experience of a designer, an intermediate solution is adopted, a simulation is meaninglessly repeated for seeking a solution which does not practically exist. Additionally, it is very difficult to determine a parameter which simultaneously satisfies a plurality of requests. As a result, it has been very difficult to understand the entity of a biological system, and extract new findings. Practically, it is assumed that although a model that indicates a health status and an ill status using the same parameter, but such a model has never been successfully realized.
The present invention processes a biological system as a constraint solving problem described in a first order predicate logic expression as described later, and obtains the presence/absence of a solution by a quantifier elimination method, a possible range of a feasible parameter, etc. The existing technology in which the quantifier elimination method is applied to a technology field such as the control technology, etc. is disclosed by the following literature.
[Patent Literature 1] Japanese Patent Application Laid-open No. Hei 11-328239 “Control System Analysis, Design Device, and Control System Analysis, and Design Processing Method”
In this literature, a problem given as a semidefinite programming (SDP) problem, or an extended semidefinite programming (ESDP) problem is formulated, the problem is converted into a first order predicate logic expression, and a solution is analytically obtained. However, in the simulation of a biological system aimed at by the present invention, it is important to obtain a feasible range of a parameter rather than to analytically obtain a solution. Therefore, it is difficult to apply this literature as is.